I am using spatstat R version version 3.0-8, to quantify spatial patterns on the distribution of solitary corals. For each sample, I am finding the following models: 1) ppm to get the CSR model , and kppm to get the best fit models for 2) for Heterogeneous Poisson using a background image file, 3) Thomas Cluster on a homogeneous background, and 4) Thomas Clusters with heterogeneous Poisson model on the background image file. I am using the minimum contrast method to compute these.

My question is: what is the most appropriate way to select which model best fits the data? I have used a goodness of fit test; but that only assesses how well the observed PCF fits the modelled PCF. Ideally I would use AIC values, but it seems (from what I can gather looking at ic(), extractAIC() and AIC.kppm()) that is isn’t possible to use AIC to compare model fits of clustered kppm model fits. Is there a way to
use AIC (or a similar measure) to compare between the four models?